1. Field of the Invention
The present invention relates to an Operational Transconductance Amplifier (OTA) comprised of Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETS) and more particularly, to a tunable OTA capable of tuning its transconductance and having the Complementary MOS (CMOS) structure, which is preferably formed on a CMOS semiconductor integrated circuit (IC).
2. Description of the Prior Art
A differential amplifier circuit having an improved transconductance linearity within a comparatively wide input voltage range has been known as an "OTA". When the transconductance is changeable, the OTA has been termed a "tunable OTA".
An example of the conventional tunable CMOS OTAs is shown in FIG. 1, in which a MOSFET is used as a common source resistor for a source-coupled differential pair of MOSFETs. This example is disclosed in the U.S. Pat. No. 5,451,901 issued in 1995.
As shown in FIG. 1, two n-channel MOSFETs M137 and M138 constitute a balanced, input differential pair of this OTA, in which gates of the MOSFETs M137 and M138 are applied with two input signals inp and inm through lines 179 and 174, respectively. Thus, a differential input signal (inm-inp) is applied across the gates of the MOSFETs M137 and M138.
Sources of the MOSFETs M137 and M138 are coupled together through an n-channel MOSFET M143 serving as a variable resistor. The sources of the MOSFETs M137 and M138 are connected to a source and a drain of the MOSFET M143 at nodes 186 and 188, respectively. A gate of the MOSFET M143 is applied with a control signal con through a line 175, so that the source-to-drain resistance of the MOSFET M143 is changed or controlled by the control signal con.
Three p-channel MOSFETs M131, M132, and M133 whose sources are coupled together and whose gates are coupled together constitute constant current sources for driving the MOSFETs M134, M137 and M138, respectively. Three n-channel MOSFETs M134, M135, and M136 constitute current mirror circuits; the MOSFETs M135 and M136 constitute constant current sources for driving the MOSFETs M142 and M141, respectively.
A bias signal pb is commonly applied to the coupled gates of the MOSFETs M131, M132, and M133 through a line 170, thereby supplying the same constant driving currents I.sub.0 to the MOSFETs M137 and M138 of the input differential pair, respectively.
Two p-channel MOSFETs M144 and M145 constitute a power down circuit for the MOSFETs M137 and M138 of the input differential pair. Sources of the MOSFETs M144 and M145 are coupled together to be connected to the sources of the MOSFETs M131, M132, and M133. Gates of the MOSFETs M144 and M145 are commonly applied with a power down signal pd through a line 176. Drains of the MOSFETs M144 and M145 are connected to drains of the MOSFETs M141 and M142, respectively. Gates of the MOSFETs M141 and 142 are connected to the drains of the MOSFETs M137 and M138 of the input differential pair, respectively.
Two output signals outp and outm are derived through the gates of the MOSFETs M139 and M140, respectively.
(N+1) n-channel MOSFETs M139 and M146(1) to M146(n) whose sources are coupled together and whose gates are coupled together constitute an output circuit for the MOSFET M139. The same n output currents 179(1) to 179(n) are derived from the drains of the M146(1) to M146(n), respectively.
Similarly, (n+1) n-channel MOSFETs M140 and M147(1) to M147(n) whose sources are coupled together and whose gates are coupled together constitute another output circuit for the MOSFET M140. The same n output currents 181(1) to 181(n) are derived from the drains of the M147(1) to M147(n), respectively.
In the conventional tunable CMOS OTA shown in FIG. 1, the MOSFET M143 provided between the sources of the input-pair MOSFETs M137 and M138 serves as a source-degeneration resistor for the input differential pair. Therefore, the transconductance of this OTA is able to be changed by changing the source-to-drain resistance of the MOSFET 143 using the control signal con applied to its gate.
Next, the operation principle of the conventional tunable CMOS OTA shown in FIG. 1 is explained below.
The currents flowing through the input-pair MOSFETs M137 and M138, which are produced by the constant current source formed by the MOSFETs M132 and M133, are equal to I.sub.0. Therefore, the input-pair MOSFETs M137 and M138 are driven by the same constant currents I.sub.0, respectively. Thus, the following equation (1) is established EQU V.sub.GS137 =V.sub.GS138 (1)
where V.sub.GS137 and V.sub.GS138 are gate-to-source voltages of the MOSESTs M137 and M138, respectively.
Therefore, if the differential input signal (inm-inp) is defined as a differential voltage V.sub.i, the differential input voltage V.sub.i is level-shifted without any change and is applied across the source and drain of the MOSFET M143. In other words, the differential input voltage V.sub.i is directly applied across the source and drain of the MOSFET M143.
Thus, drain currents I.sub.D139 and I.sub.D140 of the MOSFETs M139 and M140 are expressed as the following equations (2a) and (2b) using the driving current I.sub.0 and a drain current I.sub.D143 of the MOSFET M143. EQU I.sub.D139 =I.sub.0 +I.sub.D143 (2a) EQU I.sub.D140 =I.sub.0 -I.sub.D143 (2b)
As clearly seen from FIG. 1, a gate-to-source voltage of the MOSFET 139 is equal to gate-to-source voltages of the MOSFETs M146(1) to M146(n) . Similarly, a gate-to-source voltage of the MOSFET 140 is equal to gate-to-source voltages of the MOSFETs M147(1) to M147(n) Therefore, the following equations (3a) and (3b)are established EQU I.sub.D139 =I.sub.D146 =I.sub.0 +I.sub.D143 (3a) EQU I.sub.D140 =I.sub.D147 =I.sub.0 -I.sub.D143 (3b)
where I.sub.D146 denotes the output currents 179(1) to 179(n) outputted from the MOSFETs M146(1) to M146(n), and I.sub.D147 denotes the output currents 181(1) to 181(n) outputted from the MOSFETs M147(1) to M147(n).
Since the transconductance of the conventional CMOS OTA shown in FIG. 1 is expressed as (I.sub.D146 /V.sub.i) or (I.sub.D147 /V.sub.i), it is seen from the equations (3a) and (3b) that the transconductance is determined by the drain current I.sub.D143 of the MOSFET M143. The drain current I.sub.D143 of the MOSFET M143 is changeable by changing the source-to-drain resistance (i.e., equivalent resistance) of the MOSFET M143, which is changed by a tuning voltage V.sub.con applied to the gate of the MOSFET M143 as the control signal con.
Accordingly, the transconductance of the conventional CMOS OTA shown in FIG. 1 is tunable by changing the equivalent resistance of the MOSFET M143 using the tuning voltage V.sub.con.
The MOSFET M143 serving as the equivalent resistor is operating in the linear or triode region. Therefore, supposing that the channel-length modulation and the body effect can be ignored, the drain current I.sub.D143 of the MOSFET M143 is given by the following well-known expression (4a). ##EQU1##
In the expression (4a), V.sub.DS143 is the source-to-drain voltage of the MOSFET M143, V.sub.GS143 is the gate-to-source voltage thereof, V.sub.TH is the threshold voltage thereof, and .beta. is the transconductance parameter thereof.
The transconductance parameter .beta. is defined as ##EQU2## where .mu. is the mobility of a carrier, C.sub.ox is the gate-oxide capacitance per unit area, and W and L are a gate width and a gate length of each MOSFET, respectively.
As described above, the source-to-drain voltage V.sub.DS143 of the MOSFET M143 is equal to the differential input voltage V.sub.i. Thus, the following equation (4b) is established. EQU V.sub.DS143 =V.sub.i (4b)
Also, supposing that the differential input voltage V is generated by two input voltages [(V.sub.i /2)+V.sub.R ] and [(V.sub.i /2)-V.sub.R ] using a reference voltage V.sub.R, the gate-to-source voltage V.sub.GS143 of the MOSFET M143 is expressed as the following equation (4c). ##EQU3##
By substituting the equations (4b) and (4c) into the equation (4a), the drain current I.sub.D143 of the MOSFET M143 is given by the following equation (5). ##EQU4##
In the equation (5), although the term 2.beta.(V.sub.con -V.sub.GS138 -V.sub.TH).vertline.V.sub.i .vertline. is a linear term with respect to the amplitude of the differential input voltage V.sub.i, i.e., .vertline.V.sub.i .vertline., the term [2.beta..vertline.V.sub.i .vertline..sup.2 ] is a nonlinear term with respect to .vertline.V.sub.i .vertline.. If the amplitude .vertline.V.sub.i .vertline. of the differential input voltage becomes large, the effect of the nonlinear term will be unable to be ignored, resulting in degradation of the transconductance linearity of the conventional tunable CMOS OTA shown in FIG. 1.
As explained above, with the conventional tunable CMOS OTA shown in FIG. 1, the linearity of the transfer characteristic of the differential input pair of the MOSFETs M141 and M142 is badly affected by the nonlinear resistance of the MOSFET M143 serving as the source-degeneration resistor. Consequently, the transconductance linearity is not satisfactory.
OTAs are essential functional blocks in analog signal processing. In recent years, the need for tunable OTAs capable of tuning the linear transconductance has been becoming stronger and stronger.